بسم الله الرحمن الرحیم.

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Presentation transcript:

بسم الله الرحمن الرحیم

رباتیک جلسه هشتم

Kinematic relations X=FK(θ) θ =IK(X) Task Space Joint Space Location of the tool can be specified using a joint space or a cartesian space description

Velocity relations Relation between joint velocity and cartesian velocity. JACOBIAN matrix J(θ) Task Space Joint Space

Jacobian Suppose a position and orientation vector of a manipulator is a function of 6 joint variables: (from forward kinematics) X = h(q)

Jacobian Matrix

Jacobian Matrix Jacobian is a function of q, it is not a constant!

Jacobian Matrix Linear velocity Angular velocity The Jacbian Equation

Example 2-DOF planar robot arm 2 1 Given l1, l2 , Find: Jacobian (x , y) l2 l1

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